Feb., 1956
IONIZATION CONSTANT OF ACETICACIDIN WATER-METHANOL
151
THE IONIZATION CONSTANT OF ACETIC ACID IN WATER-METHANOL MIXTURES AT 25' FROM CONDUCTANCE MEASUREMENTS BYTHEODORE SHEDLOVSKY AND ROBERT L. KAY Contribution from the Laboratories of the Rockefeller Institute for Medical Research, N e w York, N . Y . Received Awusl 17, 1966
Data are reported on the conductances of dilute solutions of hydrochloric acid and of acetic acid in water-methanol 801vent mixtures from 10 to 100% methanol at 25'. From these and supplementary data on the difference between the conductances of sodium chloride and sodium acetate solutions a t the same concentration and the same solvent composition, values for A0 and the ionization constants K are computed for both acids. Hydrochloric wid shows evidence of some association in the methanol-rich solvents, reaching a value of K = 0.059 in methanol. Acetic acid decreases in strength from a value of K = 1.753 X 10-6 in water to K = 2.37 X in methanol. Unlike salts, which exhibit relatively flat minima in honear the middle of the water-methanol composition region, which is not inconsistant with the changes in the viscosit of the solvents, the corresponding curves for the acids fall to a minimum at about 90% methanol by weight, beyond w h i d the curves rise sharply.
Studies on the electrochemical behavior of glass membranes in buffered water-methanol mixtures over the entire range of solvent composition require for their interpretation a knowledge of the ionization constants of the weak acid components in the buffer systems employed. Such constants also can serve the practical purpose of establishing pH scales in the mixed solvents. In this paper we shall report values for the ionization constants of acetic acid at 2 5 O , derived from electrical conductance measurements covering the complete range of water-methanol composition. Ionization constants for acetic acid in watermethanol mixtures, derived from electromotive force measurements have been reported by other workers,l-a but since the 'solvent composition range was too narrowlpa for our purposes, or the glass electrode itself was used,2 and since an independent method, based on different theoretical considerations and assumptions, is desirable in any case, we chose the conductivity method. From the data presented, which include measurements on dilute solutions of acetic acid and of hydrochloric acid, the limiting equivalent conductances, as well as the ionization constants, are obtained. Theoretical The extrapolation of conductance data on weak electrolytes for determining the limiting equivalent conductance, A,, and the ionization constant K can be achieved by means of equations derived by combining the mass action law, the DebyeHuckel activity equation, and an expression for the degree of ionization, obtained either from a synthesized hypothetical conductance function for the ionized part of the weak electrolyte4 or from the measured conductance on the weak electrolyte itself.6 In this paper we shall, in a sense, combine both of these methods, by obtaining values of A0 for acetic acid synthetically from the A0 conductances on (1) H. 8 . Harned and N. D. Embree, J . Am. Chem. SOC.,67, I669 (1935). (2) A. L. Bacarella, E. Grunwald and H. P. Marshall. J . O w . Chem., 20, 747 (1955). (3) L. J. Minnick and M. Kilpatrick, THISJOURNAL, 4% 259 (1939). (4) D. A. MrcInnes and T. Shedlovsky, J . Am. Chsm. Soc., 64, 1430 (1932). (5)mR. M. Fuoss, i b i d . , KT, 488 (1935); T. Shedlovsky. J . Franklin Inat., 826, 739 (1938); R. M. Fuoss and T. Shedlovaky, J . Am. Chem. SOC.,71, 1496 (1949).
hydrochloric acid, sodium acetate and sodium chloride and using the Fuoss-Shedlovsky weak electrolyte type of conductance equations16with the A. already thus determined, for obtaining the ionization constants K . The reason for this procedure is that for electrolytes as weak as acetic acid is in water-methanol mixtures the extrapolated values for A0 by the Fuoss-Shedlovsky equations, which are linear with a slope of 1/KAo2, cannot be obtained with sufficient accuracy to yield values of K within the degree of precision we desire. The degree of ionization x is obtained by solving the conductance equation, quadratic in 2'1' in which c is the concentration and a = 8.203 X 106/(DT)'/z;p = 82.43/q(DT)'/1are the Onsager coefficients which involve the dielectric constant (D), the viscosity (q) and the absolute temperature ( T ) . The solution for equation 1 is x = -A S
AD
where S E (Z/2
+4 1 + (Z/2)9* and Z = + B l/cn ffA0
A0'12
For the measurements reported in this paper S = 1 Z is a sufficient approximation. The mass action equation we require is
+
K=-
cxy 1-x
where the activity coefficient (f) is given by the Debye-Huckel equation in which
-1ogf
= afix
(3)
a = 3.649 X 108
(DT)% By combining (1') with (2) there is obtained the weak electrolyte conductance equationK
-1= - + 1 AS
A0
CAS? KAoa
(4)
for which f 2 is computed from equations 1' and 3. However, as we have mentioned above, a plot of l / A S vs. CAXf" involves, in effect, too long an extrapolation for obtaining AO and, therefore, K with sufficient accuracy unless A0 can be more accurately determined from other data.
THEODORE SHEDLOVSKY AND ROBERT L. KAY
152
One of the most serious difficulties in conductance work with weak acids is the matter of the appropriate solvent conductance correction. Unlike the case of unhydrolyzed salts, in which the measured solvent conductance is simply subtracted from the corresponding conductance measurements on the solutions, the acids present a special problem in this respect. If the solvent conductance is all due to a weak acid (such as COz or the solvent itself) which is so much weaker than the one to be measured that its ionization can be neglected in the stronger acid medium, no solvent correction need be applied. If, on the other hand, the solvent conductance is due almost entirely to neutral salt, then this solvent conductance should be subtracted. An alkaline impurity would add to this complication still further, of course. I n the present research we have taken care to work with solvents as reasonably free from impurities as was practicable and to exclude atmospheric COz with hydrogen. The solvent correction, if any, was then determined in the following manner rather than from the measured solvent conductance which was, of course, also obtained. By combining the square root of mass action equation 2 and equation l', and substituting the definition for the equivalent conductance, A
.
L-Lo A=------C
and
(5)
A* = L / C
(5')
in which L and Loare one thousand times the measured specific conductance and solvent conductance, respectively, we obtain Since the factor in brackets on the right, the degree of association, was never too far from unity in most cases, we have used, as a first approximation L-Lo=-
AoK'/%'/%
Sf
[
~i..~s]~/¶ (6')
From plots of equation 6' and 6, which were linear, Lo, the solvent correction X lo3 was obtained. Also, from the slopes of the graphs, K could be computed once we knew Ao. For this purpose, we made use of our measurements on dilute solutions of HC1, using plots of &' E [ A 4- B
